Effective proton-neutron interaction near the drip line from unbound states in 25,26 F

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The F26 nucleus, composed of a deeply bound π0d5/2 proton and an unbound ν0d3/2 neutron on top of an O24 core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a Jπ=11+-41+ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The Jπ=11+,21+,41+ bound states have been determined, and only a clear identification of the Jπ=31+ is missing. Purpose: We wish to complete the study of the Jπ=11+-41+ multiplet in F26, by studying the energy and width of the Jπ=31+ unbound state. The method was first validated by the study of unbound states in F25, for which resonances were already observed in a previous experiment. Method: Radioactive beams of Ne26 and Ne27, produced at about 440AMeV by the fragment separator at the GSI facility were used to populate unbound states in F25 and F26 via one-proton knockout reactions on a CH2 target, located at the object focal point of the R3B/LAND setup. The detection of emitted γ rays and neutrons, added to the reconstruction of the momentum vector of the A-1 nuclei, allowed the determination of the energy of three unbound states in F25 and two in F26. Results: Based on its width and decay properties, the first unbound state in F25, at the relative energy of 49(9) keV, is proposed to be a Jπ=1/2- arising from a p1/2 proton-hole state. In F26, the first resonance at 323(33) keV is proposed to be the Jπ=31+ member of the Jπ=11+-41+ multiplet. Energies of observed states in F25,26 have been compared to calculations using the independent-particle shell model, a phenomenological shell model, and the ab initio valence-space in-medium similarity renormalization group method. Conclusions: The deduced effective proton-neutron interaction is weakened by about 30-40% in comparison to the models, pointing to the need for implementing the role of the continuum in theoretical descriptions or to a wrong determination of the atomic mass of F26.